Elimination Method Questions 9

In this page elimination method questions 9 we are going to
see solution of ninth problem from the worksheet elimination method
worksheet.

Question 9

Solve the following system of linear equations by elimination-method

15/ x + 2/y = 17 , 1/x + 1/y = 36/5

Solution:

15/ x + 2/y = 17

1/x + 1/y = 36/5

Let 1/x = a and 1/y = b

15 a + 2 b = 17 -------- (1)

a+b = 36/5

5(a+b)=36

5 a + 5 b = 36 -------- (2)

There
are two unknowns in the given equations. By solving these equations we have
to find the values of a and b. For that let us consider the coefficients
of x and y in both equation. In the first equation we have + 15a and in
the second equation also we have + 5a and the symbols are same so we have to subtract them for eliminating the variable a.

15 a + 2 b = 17

(2) x 3 => 15 a + 15 b = 108

(-) (-) (-)

----------------

-13 b = -91

b =
91/13

b = 7

now we have to apply the value of b in either given equations to get the value of another variable x

Substitute b = 7 in the first
equation

15 a + 2(7) = 17

15 a + 14 = 17

15 a = 17 – 14

15a = 3

a = 3/15

a = 1/5

Solution

x = 5

y = 1/7

verification:

15/ x + 2/y = 17

15/5 + 2/7 = 17

3 + [2/(1/7)] = 17

3 + 14 = 17

17 = 17 elimination method questions 9 elimination method questions 9

Need to try other questions:

Solve each of the following system of equations by elimination-method.